Mrs May said that following the publication of the Government’s white paper agreed at Chequers, it is “now for the EU to respond”.

She added: “Not simply to fall back on to previous positions which have already been proven unworkable. But to evolve their position in kind.

“And, on that basis, I look forward to resuming constructive discussions.”

Mrs May restated her implacable opposition to the EU backstop, which she said would involve the creation of a customs border within the UK, which was “something I will never accept and I believe no British prime minister could ever accept”.

Equally, she said that a hard border between Northern Ireland and the Republic was “almost inconceivable”.

Twenty years after the Good Friday Agreement, the return of any form of physical checkpoints or other infrastructure would be “an alien concept”.

Mrs May said that her White Paper proposals, which would see the UK remain within the single market for goods and adopt a “common rule book” of regulations with the EU, represented a “credible third option” that would “honour the Belfast Agreement, deliver on the referendum result and be good for our economy”.

The tough stance by Mrs May clearly worried EU chief negotiator Michel Barnier who said that the “drama” needed to be removed from the Northern Ireland issue.

But he said the backstop arrangement in the final agreement would “not necessarily be ours” but insisted there must be one.